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Many fundamental results in quantum foundations and quantum information theory can be framed in terms of information-theoretic tasks that are provably (im)possible in quantum mechanics but not in classical mechanics. For example, Bell's theorem, the no-cloning and no-broadcasting theorems, quantum key distribution and quantum teleportation can all naturally be described in this way. More generally, quantum cryptography, quantum communication and quantum computing all rely on intrinsically quantum information-theoretic advantages. Much less attention has been paid to the information-theoretic power of relativistic quantum theory, although it appears to describe nature better than quantum mechanics. This talk describes some simple information-theoretic tasks that distinguish relativistic quantum theory from quantum mechanics and relativistic classical physics, and a general framework for defining tasks that includes all previously known (im)possibility theorems and raises many open questions. This suggests a new way of thinking about relativistic quantum theory, and a possible new approach to defining non-trivial relativistic quantum theories rigorously. I also describe some simple and surprisingly powerful applications of these ideas to cryptography, including a new secure scheme for simultaneously committing to and encrypting a prediction and ways of securely "tagging" an inaccessible object so as to guarantee its position.